Argue with socialite Matthew regularly spurned (6)
I believe the answer is:
debate
'argue' is the definition.
('debate' can be a synonym of 'argue')
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for debate that I've seen before include "Discuss with opposing arguments" , "Exchange of views" , "Formal discussion through argument" , "Discuss; argue" , "Discuss formally" .)